Numerical phases have rich cultural connotations and connect closely with culture. Along with the extension of China's reform and opening up policy, cross-cultural communication tends to be wider. The comparative research on cross-cultural languages is very important. Because of different cultural backgrounds, the cultural connotations of Chinese…

The purpose of this study was to extend the research on the "Tests of Early Numeracy" (TEN) by following a cohort of 61 students from kindergarten through first grade. Specifically, this study examined the relationship between kindergarten and first-grade TEN measures built within and across school years and their predictive validity of a math…

Numeral-incorporating roots in the numeral systems of Argentine Sign Language (LSA) and Catalan Sign Language (LSC), as well as the main features of the number systems of both languages, are described and compared. Informants discussed the use of numerals and roots in both languages (in most cases in natural contexts). Ten informants took part in…

We compute in three different ways the same definite parametric integral. By-products are the derivation of a combinatorial identity and two integral presentations of Catalan numbers. One of them leads to a presentation using the [gamma] function.

The mysteries of mathematics are not easily revealed. Much of present day school mathematics is the product of years, sometimes centuries, of inquiring, wrestling and discovering by men of the highest intellect. The number "i" (designation for the square root of -1) is no exception. This article presents a lesson on the need for "i".

This article discusses a triangle of numbers that are related to the derangement numbers. These numbers satisfy a Pascal-like recurrence relation with subtraction instead of addition. We describe how they relate to numbers studied by other authors and use them to generalize Euler's famous recurrence relation for the derangement numbers.

Macroscopic objects, although quantum mechanical by nature, conform to Newtonian mechanics under normal observation. According to the quantum mechanical correspondence principle, quantum behavior is indistinguishable from classical behavior in the limit of very large quantum numbers. The purpose of this paper is to provide an example of the…

The paper describes the history of how learning trajectories (LTs) were associated with the Common Core State Standards for Mathematics (CCSS-M) and discusses the degree to which the two correspond faithfully. It reports on a website, www.turnonccmath.com, which organizes the K-8 standards into 18 LTs describing the development of big ideas over…

Children's drawings are one of the most appropriate approach to knowing children, their individuality and also their perceptions. Child is not always able to express their thoughts precisely, because their vocabulary is still incomplete and is gained just lately. In our paper we concentrate on drawing as a communication means, with which we can…

This article addresses an important problem of graphing quantitative data: should one include zero on the scale showing magnitude? Based on a real time series example, the problem is discussed and some recommendations are proposed.

Converging behavioral and neural evidence suggests that numerical representations are mentally organized in left-to-right orientation. Here we show that this format of spatial organization extends to emotional expression. In Experiment 1, right-side responses became increasingly faster as number (represented by Arabic numerals) or happiness…

The purpose of this article is to explore student-generated connections among counting problems. The literature indicates that such problems pose difficulties for students, who struggle to detect common structures and identify models of underlying problem types. A case study is presented here, in which students elaborate upon connections they make…

This paper builds from a prior study into the teaching and learning of basic number facts in New Zealand. It reports the changes in practice of one teacher that were brought about by her reflection on the effectiveness of her teaching and learning programme. It details how this teacher created a process which helped make the learning of basic…

In light of recent reform recommendations, teachers are expected to turn proofs and proving into an ongoing component of their classroom practice. Two questions emerging from this requirement are: Is the mathematical knowledge of high school teachers sufficient to prove various kinds of statements? Does teachers' knowledge allow them to determine…

Difficulties in visual attention are increasingly being linked to dyslexia. To date, the majority of studies have inferred functionality of attention from response times to stimuli presented for an indefinite duration. However, in paradigms that use reaction times to investigate the ability to orient attention, a delayed reaction time could also…